BSc (Hons) Mathematics

Applied Mathematics

This module introduces students to the study of the motion of bodies (including the special case in which bodies remain at rest) in accordance with the general principles first articulated by Sir Isaac Newton and Galileo Galilei. Applied mathematics has many important applications in science, such as physics, astronomy, chemistry, Geology and engineering as well as being of great significance outside the realm of science.

Calculus I

This module builds on the material covered at A level and introduces some new fundamental areas of mathematics. Differential Calculus will be extended and you will start the study of the applications of differentials, as you learn to apply these to a variety of contexts including optimisation problems.

Calculus II

This module builds on the material covered at A level and introduces some new fundamental areas of mathematics. You will explore Integral Calculus in more detail and begin to study of the applications of integrals. These techniques will be applied to a variety of contexts including area and volumes.

Complex Numbers and Differential Equations

This course begins with the introduction of a new number: the square root of minus 1. Throughout the module, you will see that working with complex numbers can often improve our understanding of certain mathematical processes and greatly simplify calculations. In the second part of the course, you will discover how to apply differential equations to model a vast array of physical phenomena and learn techniques for solving them.

Discrete Mathematics

The content of all the mathematics modules follows the overarching principle of developing students’ technical ability, development of knowledge into areas of mathematical structure, proof and formality, continuity, discrete procedures, limiting processes, mathematical modelling and interpretation of space. This module’s content will be taken from mathematical techniques/areas such as languages, automata, and grammars; finite-state and Turing machines; ordered sets; lattices; set theory; functions; countable and uncountable sets; combinatorics; recurrence relations.

Introduction to Statistical Theory

Statistics involves the analysis and interpretation of data with a view to making more informed decisions. As such, its importance in the 21st century can hardly be overstated: statistical techniques are fundamental tools in Data Science, Economics and Biology, to name a few.

In this module, you will gain an introduction to statistical inference and investigate topics such as point and interval estimation, hypothesis testing, and regression models.

Linear Algebra

This module introduces you to modelling using systems of linear equations, basic and advanced matrix algebra.

Probability and Random Variables

This module provides a grounding in the theory of probability, and is an essential precursor for the subsequent study of mathematical statistics and operations research.

The emphasis will be on modelling real situations, including probability calculations motivated by statistical problems.

Applications of Probability

This module aims to develop techniques in the use of probability in real-world contexts. Exploration of the theoretical mathematical models used to describe patterns of events that occur in time, and in space.

Calculus III

This module builds on the material covered within the first year calculus courses. Calculus will be extended to functions of more than one variable and applications of partial differentiation and multiple integrals.

Complex Analysis

This module explores how complex analysis is concerned with extending the familiar notions of differentiation and integration to functions of a complex variable. Perhaps surprisingly, this apparent increase in sophistication results in a host of spectacularly strong results. Applications abound; aside from techniques that reduce seemingly impossible integrals to straightforward calculations, complex analysis also underpins the notion of Fourier transform, which is central in various branches of physics and engineering.

Further Applied Mathematics

Building on the techniques introduced in your first year applied mathematics module, this looks to develop a deeper understanding of the field of applied mathematics.

Group Theory

This modules explores how groups were introduced in an attempt to study one of the most fundamental aspects of nature: symmetry. As an example, the 6 symmetries of an equilateral triangle form a group: every symmetry has a counterpart inverse symmetry, and any two symmetries can be combined to obtain another. Since the concept of symmetry is so widely applicable, the theory of groups touches almost every branch of pure and applied mathematics.

Mathematical Analysis

The subject of mathematical analysis puts calculus on a rigorous foundation. The key concept underlying the whole course is that of “limit”. The purpose of analysis is to develop a solid understanding of when familiar techniques of calculus apply and what can go wrong when they do not.

As the module develops, you will study topics such as the convergence of sequences and series, the continuity of functions, and the operations of differentiation and integration.

Network Analysis

In recent years, interest in the theory of complex networks has exploded. The advent of social media and progress in artificial intelligence have made network analysis into an indispensable tool.

In this course, you will study the mathematical theory that underlies network analysis; namely, graph theory. Graph theory is an exciting and rich subject in its own right and many of its results and principles will be studied in this module.

Statistical Methods

In this module, you will build on the material introduced in the first-year module to take a more in-depth look at the idea of estimation.

You will learn how to compare the relative strengths and weaknesses of estimators and how you would find good estimators.

We will guide you as to how to answer, as this is crucial to being able to make sensible predictions from given datasets.

Time Series Analysis

This module introduced you to the concept of a time series: a sequence of data that has been recorded in time order.

The goal of this module is to try and understand how consecutive data points in a time series are dependent on each other. This dependence then allows us to create statistical models which can be used to forecast future values.

Advanced Calculus

This module aims to extend familiar notions from calculus to settings that involve functions of more than one variable.

The resulting subject, known as vector calculus, is fundamentally important in branches of applied mathematics such as fluid dynamics and electromagnetism. One of the central results of the course is Stokes’s Theorem, which ties together many of the concepts studied.

Advanced Game Theory

Game theory tries to model how decision makers interact during situations of conflict or cooperation.

The implications of this theory are widespread and have had a significant impact on many subjects including economic, biology and computer sciences.

Applied Statistics

This module will equip you with a range of techniques used regularly by practising statisticians.

In addition to discussing the mathematical theory behind these techniques, the module also introduces statistical software that can be used to conduct them. The material covered, together with that taught in earlier years, is fundamental if you are looking to enter a career involving data analysis and interpretation.

Machine Learning

Within this module, you will study algorithms that allows computers to learn and improve from experience.

The importance of this topic to many modern technologies cannot be overestimated.

Mathematics Project

As a result of initial planning and negotiation, a learning contract will be drawn up between individual students and the module co-ordinator. The content will, therefore, be negotiated in the light of identified needs.

Number Theory

Number theory is the study of whole numbers. Number facts have intrigued most people at some stage in their education, and in addition to its inherent fascination, number theory has turned out to have practical applications in recent years such as encryption. You will explore the historical theories around numbers and critically engage with the literature that surrounds them.

Operations Research

Operations research is simply a quantitative approach to decision making that seeks to best design and operate a system (in this case an organisation of interdependent components) usually under conditions requiring the allocation of scarce resources. Elements of OR have been covered in previous modules and this module is designed to bring these elements together to create a suite of decision making tools.

Optimisation

This module explores the methods, theories, and applications of optimisation.

You will study:

• Iterative Methods and errors
• Root finding
• Systems of linear equations
• Gaussian elimination
• Matrices and LU decomposition
• Vector and matrix norms
• Ill-conditioning
• Induced stability
• Systems of non-linear equations.